A journey down the rabbit hole of Rubik's-style puzzles

A few days ago, Deadesq (AIC’s first guest blogger) mentioned to me that he was looking for a more efficient solution to the four-headlight situation. By four headlights, he meant the situation in which, after applying the Beginner’s Method PLL corner permutations, you’re left with all four faces having headlights — with no fully solved side face. As I described in my tutorial, in that situation, the Beginner’s Method requires applying the PLL edge permutation algorithm twice in a row. Although I can do that quickly, it’s still not as quick as a single permutation. Enter H and Z perms….

H and Z perms (permutations) allow trading both pairs of edges at once — H when the pairs are opposite one another, and Z when the pairs are adjacent. Here are the two situations and algorithms:

H Perm

(M2 U) (M2 U2) (M2 U) M2

Z Perm

(M2 U) (M2 U) (M’ U2)(M2 U2) (M’ U2)

I had never really tried or thought about M moves before. An M move is applied to the vertical layer between the left and right faces, and matches the L face in terms of turn direction. In other words, an M means moving the top of the middle layer toward the front; an M’ means moving the top of the middle layer toward the back. Although it took me a while to figure out the mechanics and to memorize the algorithms, after just about thirty minutes, I was able to do the H in under three seconds and Z in under five:

After a while, I settled on using my left hand ring or middle finger to flick the middle layer from underneath to do M’ turns. The video on the right shows me performing the move in slow motion.

In terms of my cubing, this challenge came just as I was hitting a floor in my solve times. I know that I can speed up my F2L times a bit, and that my mechanics and finger tricks can use some fine tuning. Those surely will amount to some small time savings. But the real time savings will come from more efficient techniques. Instead of serially applying some of the Beginner’s Method algorithms (some up to three times each), algorithms like the H and Z perms allow for more efficiency, speed, and fluidity. As I’m not particularly good at memorizing large chunks of information out of context, learning a couple PLL perms at a time seems like the ticket. These were good tools to add to the chest.